There are 16 4-player minigames in Mario Party 4, many of which focus around rapidly pressing a button. Only one of the sixteen is a coin-collecting bonus game, where everyone can earn coins.
Avalanche!
Rules: Don't get swallowed by the avalanche behind you! Ski down the mountain and avoid the obstacles too!
Controls: 
: Turn
: Use poles for speed
Advice: If you don't use your poles, you'll slow down. Watch out for the walls and boulders as you speed down the hill.
The winner of this game is the person who reaches the end of the course first, even if other players are still alive. You'll want to tap just about nonstop during the minigame. The boulders and jumps are always in the same positions. The first jump is on the characters' left, the first rock is on their right, the next rock is in the middle, and the final rock is on their right. This gives Player 1 a slight advantage, as they start in a position where there are very few obstacles. Make sure that you don't stay too close to the wall, as it will slow you down as well.
Bob-omb Breakers
Rules: Connect three like shapes to make them disappear. Remember, you can also play in other people's areas. First one to 100 points wins.
Controls: : Move Blocks
: Rotate Clockwise
: Rotate Counterclockwise
: Flip Over
Advice: Bob-ombs explode when surrounded by blocks. You get more points for combos. Make sure to play in your opponents' areas!
As the advice states, the easiest way to earn points is to make combos, where one set of three causes other blocks to fall into the right places. When you've got something in the position you want, you can press down on the control stick to make it fall faster. You earn one point for every shape in a group, and this amount is multiplied by 2, 4, 8, etc. depending on how long a chain has been going. If you see an opponent setting up a combo, you can steal it by moving into their territory, if you're fast enough. Bob-ombs are also a good source of points. They're worth 1 point multiplied by the number of blocks surrounding them. This means that a bob-omb on the bottom would only be worth 5 points, while a higher up one would be worth 8. A player who's entire area is filled will be unable to play until some blocks are cleared.
Booksquirm
Rules: Avoid getting flattened by the pages! Find a hole in the falling page and position yourself so you fit through to the next page!
Controls: : Move
Advice: Look for shadows in the falling page to find the passage to the next page.
Whenever possible, try and position yourself under a hole in the middle, so you can reach both sides easily. Be careful of your opponents, as higher-level computers will frequently try to push you out of the safe zone. Watch out for the moon shapes, as only two people can fit under them easily. If you see that your character is starting to get squashed and is near a safe zone, you can actually survive the attack by adjusting your position quickly. As it gets faster and faster, it comes down more and more to luck, as to which character has a shorter distance to a safe zone. Though the game starts with three holes per page, there will only be two holes by the tenth page, and just one hole starting at the sixteenth. When in doubt, watch the shadows.
Domination
Rules: Press the switch repeatedly to set up your Whomp dominoes.
Controls: : Tap the Switch
Advice: Press as fast as you can for 10 seconds.
This game is very simple; simply mash the A button for ten seconds. Compared to Slime Time, the computers are much better at this game, with Expert computers frequently getting scores above 100. There is an award in the Present Room for getting a record of more than 100 taps.
Long Claw of the Law
Rules: Catch the character shown in the wanted poster three times to win.
Controls: 
: Rotate Right
: Rotate Left
: Move Up and Down
: Catch Character
Advice: The wanted character is hidden behind a door. When you can't find him, either wait for a door to open or look at another door.
Move quickly, but don't skip any doors. There will be Bob-ombs, Boos, Chain Chomps, Goombas, Shy Guys and Thwomps, but only one type will be wanted. While waiting for a door to open, quickly scroll back and forth between two screens until you identify the character. At the edges of your screen, you can see how many doors are currently open on the next screen. Be careful not to mix up Chain Chomps and Bob-ombs, as they are both the same color. Efficiency is everything in this game, so move forward in a methodical manner, except when you cycle between two screens. Don't backtrack unless you're sure you've missed something. There will be exactly three of the wanted character, so you can't afford to miss anyone.
Manta Rings
Rules: Dive through the rings while swimming in the ocean. Each ring is worth one point. If any enemies hit you, you'll lose points.
Controls: : Move
: Press repeatedly to go forward
Advice: The gold Manta rings are worth three points, so try to grab as many gold ones as you can!
The best strategy in this game is to go after chains of rings. Frequently, there will be several rings more or less in front of each other, worth 3 or 4 points. Stay at the back, dodging enemies until a chain of rings and/or a gold ring appears. When there aren't any chains, simply go after the rings that the other players ignored. If a second player stays at the back of the screen with you, swim slightly ahead of them so that you can get to the rings before them.
Mario Medley
Rules: Breaststroke, Backstroke, and Crawl. You must do a 25-meter lap of each different stroke to win this race.
Controls:+ (Simultaneously): Breaststroke
+ (Alternately): Backstroke
+ (Alternately): Crawl
Advice: If you swim too hard, you'll get tired, so watch your heart meter carefully!
This game is more than just a button-masher because of the heart meter. If it depletes entirely, you will greatly slow down, almost to a complete stop. When you first start off, swim fast enough to deplete about a third of the heart. From there, maintain a steady pace until the last half of the Crawl. Swim as quickly as you can, slowing down only if the heart is in danger of emptying. There is an award in the Present Room for getting a record time of under 1'00".
Mario Speedwagons
Rules: Time to race on the speedway! Step on the gas when the light turns green!
Controls: : Accelerate
: Change Gears
(When your meter starts blinking, it's time to shift gears.)
Advice: You can hit the gas a little before the green light for a good start. If you overdo it, you will spin out and ruin your start.
Winning this game is all about starting at the right time. You'll want to start holding about halfway between the second yellow light and the green light. Simply press whenever your controller rumbles. If you get a good start, you should be able to win.There is an award in the Present Room for getting a record time of under 10.00". A perfect time is widely accepted to be 9.15".
Mr. Blizzard's Brigade
Rules: Run on this frozen pond while avoiding the snowballs thrown by the Blizzards.
Controls: : Move
Advice: Move right before the Blizzards throw their snowballs. They'll stop moving just before they throw.
The Blizzards will look toward a character before they fire their snowballs. For the first 15 seconds or so, don't move unless a Blizzard targets you. After that point, you'll want to keep moving around the rim of the arena, but stay away from other character's. As characters get frozen, they serve as obstacles that you have to move around, but they can also serve as shields. Whenever you see a giant snowball or "snow boulder", you'll want to watch its shadow and stay as far away from it as you can. As the match goes on, the snowballs will come more and more frequently. Whenever possible, try and direct the attacks onto the other player by pushing them.
Paratrooper Plunge
Rules: This is a coin-collecting bonus game! If you run into enemies four times, you're out.
Controls: : Move
Advice: Move around while you're falling to get the most coins and avoid all the enemies.
The reasons to avoid the enemies are two-fold: not only can they cause you to be eliminated, but they stun you and prevent you from collecting coins. When possible, bump opponents into Paratroopas or Shy Guys, especially those opponents that have almost been eliminated. If you're quick, it's possible to get twp coin bags at each of the coin bag clusters. Overall, prioritize evasion before you go after the coins. Even if you don't get the most coins, every single one helps.
Photo Finish
Rules: Controls: Advice:
Slime Time
Rules: Escape from the Slime! Be the first person to reach the middle platform to win!
Controls: : Press quickly to escape
Advice: If you don't go fast enough, you'll be pulled back into the Big Slime, so don't give up until you're done.
This is probably the easiest of the button-mashing minigames speed-wise and length-wise. Focus on going just fast enough so that you won't get pulled back; the computer players almost always get pulled back at least once. Keep in mind that as you get closer to the finish, your character will move more slowly, and you will need to tap more quickly to avoid getting pulled back. Frequently, this minigame ends in under 10 seconds.
Stamp Out!
Rules: Controls: Advice:
Take a Breather
Rules: Controls: Advice:
Three Throw
Rules: Controls: Advice:
Toad's Quick Draw
Rules: Controls: Advice: